Ms McGovern, the Wirral South MP, had been asked to take part in Labour's policy review on child poverty and combating inequality. She was due to meet Mr McDonnell for a second time to discuss the issue on Wednesday.
"We are all Labour members and we believe in having a Labour government. That's what we are, nothing more nothing less.
"And, as I say, I don't want to be on the telly talking about this but I have been backed into a corner and I have got no other choice now but to stand up and say 'this is who we are' and we should just get on with the business of getting a Labour government."
It came as Mr Corbyn defended his reshuffle, writing in the Observer that it had led to a “more diverse” front bench.
He said: “For all the media sound and fury, last week’s shadow cabinet reshuffle has made us a stronger, more diverse and more coherent leadership team.
“Along with the huge increase in our party membership in the past six months, it will help make Labour a more effective champion of the people who need us to give them a voice, to win elections and change our country for the better.”
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